There are two possible ways this application will be developed. The first one is to try to do something like www.picnik.com, image processing directly on the browser.
The other is to develop CBIR (content-bases image retrieval) algorithms.

So, is it possible to send an image from a PHP script to an OpenCV program? Or even display the image being manipulated in real time?

Depends on both server restrictions and the target program. If server allows, you can run external programs and pass arguments to them.

These external programs are usually CLI programs, i.e., without GUI. Image would be passed as a path to an image file (rather than data about pixels), i.e., my_opencv_program -resize 1024x768 -infile /tmp/input.jpg -outfile /tmp/output.jpg.